5 ( five ) is a number, numeral system, and glyph. It is the natural number following 4 and preceding 6.
In mathematics
Five is the third
prime number. Because it can be written as , five is classified as a
Fermat number; therefore a
regular polygon with 5 sides (a regular
pentagon) is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first
safe prime, the third
Catalan number, and the third
Mersenne prime exponent. Five is the first
Wilson prime and the third
factorial prime, also an alternating factorial. Five is the first
good prime.
It is an
Eisenstein prime with no imaginary part and real part of the form . It is also the only number that is part of more than one pair of
. Five is a
congruent number.
Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.
Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3.
The number 5 is the fifth Fibonacci number, being plus . 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... ( lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth .
5 is the length of the hypotenuse of the smallest integersided right triangle.
In bases 10 and 20, 5 is a 1automorphic number.
Five is the second Sierpinski number of the first kind, and can be written as S2 = (2^{2}) + 1.
While polynomial equations of degree and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group S_{ n} is a solvable group for and not solvable for .
While all graph theory with 4 or fewer vertices are planar graph, there exists a graph with 5 vertices which is not planar: K_{5}, the complete graph with 5 vertices.
There are five .[Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61]
A polygon with five sides is a pentagon. representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.
Five is the only prime number to end in the digit 5 because all other numbers written with a 5 in the ones place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1automorphic number.
Vulgar fractions with 5 or in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or .
There are five Exceptional Lie groups.
List of basic calculations


5 × x  5  10  15  20  25  30  35  40  45  50
!  55  60  65  70  75  80  85  90  95  100 


5 ÷ x  5  2.5  1.  1.25  1  0.8  0.  0.625  0.  0.5
!  0.  0.41  0.  0.3  0. 
x ÷ 5  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  2
!  2.2  2.4  2.6  2.8  3 


5  5  25  125  625  3125  15625  78125  390625  1953125  9765625
!  48828125  244140625  1220703125  6103515625  30517578125 
x  1  32  243  1024  3125  7776  16807  32768  59049  100000
!  161051  248832  371293  537824  759375 
In the powers of 5, every power ends with the number five and from 5^{3}, if the exponent is odd, then the hundreds digit is 1; instead, if it is even, the hundreds digit is 6.
Evolution of the glyph
The evolution of the modern Western
glyph for the numeral 5 cannot be traced back to the Indian system as for the numbers 1 to 4. The
Kushan Empire and
Gupta Empire empires in what is now
India had among themselves several different glyphs which bear no resemblance to the modern glyph. The
Devanagari and
Punjabi language took these glyphs and all came up with glyphs that are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5.
[Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65] It was from those characters that Europeans finally came up with the modern 5.
While the shape of the 5 character has an ascender in most modern , in typefaces with text figures the character usually has a descender, as, for example, in .
Science

The atomic number of boron.

The number of appendages on most sea star, which exhibit pentamerism.

The most destructive known tropical cyclone rate as Category 5 on the Saffir–Simpson hurricane wind scale.

The most destructive known rate an F5 on the Fujita scale or EF5 on the Enhanced Fujita scale.
Astronomy

Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.

The New General Catalogue object NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda.

The Roman numeral V stands for dwarfs (main sequence stars) in the Yerkes spectral classification scheme.

The Roman numeral V (usually) stands for the fifthdiscovered satellite of a planet or minor planet (e.g. Jupiter V).

There are five in a twobody system.
Biology

Perception is conceived to occur through five senses.

Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.
Computing

5 is the ASCII code of the Enquiry character, which is abbreviated to ENQ.
Religion and culture
Hinduism

The god Shiva has five faces and his Mantra is also called Panchakshari (Five Worded) mantra.

The goddess Saraswati, goddess of knowledge and intellectual is associated with Panchami or number 5.

There are five elements in this universe: Dharti, Agni, Jal, Vayu evam Akash (Earth, Fire, Water, Air and Space respectively).

The most sacred tree in Hinduism has 5 leaves in every leaf stunt.

Most of the flowers have 5 petals in them.
Christianity
Discordianism

In Discordianism, 5 is seen as a very important number. This is demonstrated in the Law of Fives, as well as in the Pentabarf, which contains five rules.

Each page of the Principia Discordia—the primary religious document in Discordianism—is labeled with five digits.
Islam

The Five Pillars of Islam

pray to Allah five times a day

According to Shia Muslims, the PanjetanePak or the Five Holy Purified Ones are the members of Muhammad's family: Muhammad, Ali, Fatimah, Hasan, and Husayn and is often symbolically represented by an image of the Khamsa.
Judaism

The Torah contains five books—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch (Greek language for "five containers", referring to the scroll cases in which the books were kept), or Humash (חומש, Hebrew language for "fifth").

The book of Psalms is arranged into five books, paralleling the Five Books of Moses.

The Hamsa, an ancient symbol shaped like a hand with four fingers and one thumb, is used as a protective amulet by ; that same symbol is also very popular in culture, known to protect from envy and the evil eye.
Sikhism

The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as panj kakars or the "Five Ks" because they start with letter K representing kakka (ਕ) in the Punjabi language's Gurmukhi script. They are: kesh (unshorn hair), kangha (the comb), kara (the steel bracelet), kachhehra (the soldiers shorts), and kirpan (the sword) (in Gurmukhi: ਕੇਸ, ਕੰਘਾ, ਕੜਾ, ਕਛਹਰਾ, ਕਿਰਪਾਨ). Also, there are five deadly evils: kam (lust), krodh (anger), moh (attachment), lobh (greed), and (ego).
tao">
Tao
Other religions and cultures

According to ancient Greek philosophers such as Aristotle, the universe is made up of five classical elements: water, earth, air, fire, and ether. This concept was later adopted by Medieval alchemists and more recently by practitioners of NeoPagan religions such as Wicca.

The pentagram, or fivepointed star, bears religious significance in various faiths including Baha'i, Christianity, Freemasonry, Satanism, Taoism, Thelema, and Wicca.

In Cantonese, "five" sounds like the word "not" (character: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.

In tradition, there are Wu Xing: (water, fire, earth, wood, and metal). The Japanese names for the weekday names, Tuesday through Saturday, come from these elements via the identification of the elements with the Classical planet. Also, the traditional Japanese calendar has a fiveday weekly cycle that can be still observed in printed mixed calendars combining Western, ChineseBuddhist, and Japanese names for each weekday.

Members of The Nation of Gods and Earths, a primarily African American religious organization, call themselves the "FivePercenters" because they believe that only 5% of mankind is truly enlightened.
Art, entertainment, and media
Fictional entities

James the Red Engine, a fictional character numbered 5.

Johnny 5 is the lead character in the film Short Circuit (1986)

Number Five is a character in Lorien Legacies

Sankara Stones, five magical rocks in Indiana Jones and the Temple of Doom that are sought by the Thuggees for evil purposes

The Mach Five ( Mahhagō?), the racing car Speed Racer (Go Mifune in the Japanese version) drives in the anime series of the same name (known as "Mach Go! Go! Go!" in Japan)

In the works of J. R. R. Tolkien, five wizards (Saruman, Gandalf, Radagast, Blue Wizards) are sent to Middleearth to aid against the threat of the Dark Lord Sauron

In the A Song of Ice and Fire series, the War of the Five Kings is fought between different claimants to the Iron Throne of Westeros, as well to the thrones of the individual regions of Westeros (Joffrey Baratheon, Stannis Baratheon, Renly Baratheon, Robb Stark and Balon Greyjoy)
Films

Towards the end of the film Monty Python and the Holy Grail (1975), the character of King Arthur repeatedly confuses the number five with the number three.

Five Go Mad in Dorset (1982) was the first of the longrunning series of Comic Strip Presents... television comedy films

The Fifth Element (1997), a science fiction film

Fast Five (2011), the fifth installment of the Fast and Furious film series.

V for Vendetta (2005), produced by Warner Bros., directed by James McTeigue, and adapted from Alan Moore's graphic novel V for Vendetta prominently features number 5 and Roman Numeral V; the story is based on the historical event in which a group of men attempted to destroy Parliament on November 5, 1605
Music
Groups

Five (band), a UK Boy band

The Five (composers), 19thcentury Russian composers

5 Seconds of Summer, pop band that originated in Sydney, Australia

Five Americans, American rock band active 1965–1969

Five Finger Death Punch, American heavy metal band from Las Vegas, Nevada. Active 2005–present

Five Man Electrical Band, Canadian rock group billed (and active) as the Five Man Electrical Band, 1969–1975

Maroon 5, American pop rock band that originated in Los Angeles, California

MC5, American punk rock band

Pentatonix, a Grammywinning a cappella group originated in Arlington, Texas

The 5th Dimension, American pop vocal group, active 1977–present

The Dave Clark Five, a.k.a. DC5, an English pop rock group comprising Dave Clark, Lenny Davidson, Rick Huxley, Denis Payton, and Mike Smith; active 1958–1970

The Jackson 5, American pop rock group featuring various members of the Jackson family; they were billed (and active) as The Jackson 5, 1966–1975

We Five: American folk rock group active 1965–1967 and 1968–1977

Grandmaster Flash and the Furious Five: American rap group, 1970–80's

Fifth Harmony, an American girl group.

Ben Folds Five, an American alternative rock trio, 1993–2000, 2008 and 2011–2013
Other uses

A perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.

Modern musical notation uses a musical staff made of five horizontal lines.

In – the fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5:1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves plus a pure major third. Thus, the interval of 5:4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a cappella vocal ensemble singing), will contain such a pure major third.

The number of completed, numbered piano concertos of Ludwig van Beethoven, Sergei Prokofiev, and Camille SaintSaëns.

Using the Latin root, five musicians are called a quintet.

A scale with five notes per octave is called a pentatonic scale.

Five is the lowest possible number that can be the top number of a time signature with an asymmetric meter.
Television
 Stations

Channel 5 (UK), a television channel that broadcasts in the United Kingdom

TV5 (Philippines) ( former TV station ABC 5) (DWETTV channel 5 In Metro Manila) a television network in the Philippines.
 Series

Babylon 5, a science fiction television series

The number 5 features in the television series Battlestar Galactica in regards to the Final Five cylons and the Temple of Five

Hi5 (Australian TV series), a television series from Australia

Hi5 (UK TV series), a television show from the United Kingdom

Hi5 Philippines a television show from the Philippines

Odyssey 5, a 2002 science fiction television series

Tillbaka till Vintergatan, a Swedish children's television series featuring a character named "Femman" (meaning five), only can utter the word 'five'.

The Five (talk show): Fox News Channel roundtable current events television show, premiered 2011. So named for its panel of five commentators.

Yes! PreCure 5 is a 2007 anime series which follows the adventures of Nozomi and her friends. It is also followed by the 2008 sequel Yes! Pretty Cure 5 GoGo!
Literature

The Famous Five is a series of children's books by British writer Enid Blyton

The Power of Five is a series of children's books by British writer and screenwriter Anthony Horowitz

The Fall of Five is a book written under the collective pseudonym Pittacus Lore in the series Lorien Legacies

The Book of Five Rings is a text on kenjutsu and the martial arts in general, written by the swordsman Miyamoto Musashi circa 1645

SlaughterhouseFive is a book by Kurt Vonnegut about World War II
Sports

The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited represented by the Olympians (Europe, Asia, Africa, Australia and Oceania, and the Americas).

In baseball scorekeeping, the number 5 represents the third baseman's position.

In basketball:

The number 5 is used to represent the position of center.

Each team has five players on the court at a given time. Thus, the phrase "five on five" is commonly used to describe standard competitive basketball.

The "5second rule" refers to several related rules designed to promote continuous play. In all cases, violation of the rule results in a turnover.

Fiveaside football is a variation of association football in which each team fields five players.

In ice hockey:

A major penalty lasts five minutes.

There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net).

The area between the goaltender's legs is known as the fivehole.

In most rugby league competitions, the starting left wing wears this number. An exception is the European Super League, which uses static squad numbering.

In rugby union:

A try is worth 5 points.

One of the two starting lock forwards wears number 5, and usually jumps at number 4 in the lineout.

In the French variation of the bonus points system, a bonus point in the league standings is awarded to a team that loses by 5 or fewer points.
Technology

5 is the most common number of gears for automobiles with manual transmission.

In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.

On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button (on computer keyboards, the 5 key of the numeric keypad has the raised dot or bar, but the 5 key that shifts with % does not).

On most , the 5 key is associated with the letters J, K, and L, but on some of the BlackBerry phones, it is the key for G and H.

The Pentium, coined by Intel Corporation, is a fifthgeneration x86 architecture microprocessor.

The resin identification code used in recycling to identify polypropylene.

A pentamer is an oligomer composed of five subunits.
Miscellaneous fields
Five can refer to:

"Give me five" is a common phrase used preceding a high five.

An informal term for the British Security Service, MI5.

Five babies born at one time are multiple birth. The most famous set of quintuplets were the Dionne quintuplets born in the 1930s.

In the United States legal system, the Fifth Amendment to the United States Constitution can be referred to in court as "pleading the fifth", absolving the defendant from selfincrimination.

Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.

Quintessence, meaning "fifth element", refers to the elusive fifth element that completes the basic four elements (water, fire, air, and earth)

The designation of an Interstate Highway (Interstate 5) that runs from San Diego, California to Blaine, Washington. In addition, all major northsouth Interstate Highways in the United States end in 5.

The five basic are sweetness, salty, sour, bitter, and umami.

In the computer game Riven, 5 is considered a holy number, and is a recurring theme throughout the game, appearing in hundreds of places, from the number of islands in the game to the number of bolts on pieces of machinery.

The Garden of Cyrus (1658) by Sir Thomas Browne is a Pythagorean discourse based upon the number 5.

The holy number of Discordianism, as dictated by the Law of Fives.

The number of Justices on the Supreme Court of the United States necessary to render a majority decision.

The number of dots in a quincunx.

The number of permanent members with veto power on the United Nations Security Council.

The number of sides and the number of angles in a pentagon.

The number of points in a pentagram.

The number of Korotkoff sounds when measuring blood pressure

The drink Five Alive is named for its five ingredients. The drink punch derives its name after the Sanskrit पञ्च (pañc) for having five ingredients.

The Keating Five were five United States Senators accused of corruption in 1989.

The Inferior Five: Merryman, Awkwardman, The Blimp, White Feather, and Dumb Bunny. DC Comics parody superhero team.

No. 5 is the name of the iconic fragrance created by Coco Chanel.

The Committee of Five was delegated to draft the United States Declaration of Independence.

The 5th U.S. President was James Monroe.

The fivesecond rule is a commonly used rule of thumb for dropped food.

555 95472, usually referred to simply as 5, is a minor male character in the comic strip Peanuts.

Number Five/#00.05 is a character from the comic book series The Umbrella Academy
See also

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 58–67
External links